Louisiana's famous 1991 "Lizard versus Wizard" Governor race

(By Warren D. Smith with a lot of help from William Poundstone.
You can also see our
overview of all LA's governor races.)

This election was a plurality plus top-2-runoff election.
It excellently illustrates the malfunction of both plain plurality voting
and runoff systems and the superiority of approval and range voting.

Instant Runoff Voting (IRV)
presumably would have behaved in essentially the same bad way
because this race was dominated by the top 3 contenders.
(IRV and plain top-2 runoff behave the same in any race with 3 candidates
if the voters are the same and act self-consistently.
Details.)

The all-time great
"better a lizard than a wizard" bumper sticker referred to the corruption
allegations that dogged Edwards throughout his career
(in 2001 he was sentenced to 10 years in prison on racketeering charges)
versus the fact David Duke
was "Grand Wizard of the Knights of the Ku Klux Klan."
(Duke also served prison time in 2003 after pleading guilty to tax evasion and mail fraud.
President Bush on 7 Nov. 1991 said David Duke was a
charlatan unfit to hold public office because he has espoused racist and neo-Nazi beliefs
[R.Suro: New York Times 7 Nov. 1991 page B18]
– thus, unusually for a Republican president,
Bush pretty much came out in favor of a Democratic candidate against a Republican.
Edwards himself, when asked what he would have to do to beat Duke, famously replied
"Stay alive."
)

Their face-off
happened when the incumbent governor Roemer
(who perhaps became unpopular
when he switched from Democrat to Republican parties while in office)
did not make the runoff.

Paradoxes

Roemer would have beaten every rival
in a head-to-head contest
(was the "Condorcet winner," also called "beats-all winner").
We base that on

A September 1991 Verne Kennedy poll asking who they'd
choose just between Roemer and Edwards. It was 46.0% for Roemer to 42.7%
for Edwards, with the rest undecided.
(Also, a 1990 phone poll of 900 random Louisianans by the Baton Rouge State Times
asking who they'd vote for in a Roemer-Edwards runoff, found 37% Roemer versus 27% for Edwards.)
Note: This also proves that a lot of Duke voters preferred Roemer over Edwards, which is not
surprising considering Edwards was the overwhelming favorite among black voters.

A poll reported in the 91-10-16 Shreveport Times (page 14A)
said that Roemer would beat Duke in a runoff.
(Also a 1990 phone poll of 900 random Louisianans by the Baton Rouge State Times
asking who they'd vote for in a Roemer-Duke runoff, found 37% Roemer versus 11% for Duke.)
Even without these latter polls we still would be fairly confident
Roemer would have beaten Duke because
Edwards' supporters
were more than half black
[e.g. "Black voters have gravitated to Mr. Edwards," R.Suro, NY Times 19 Oct. 1991 page 1.1;
"Polls show him getting up to 90 percent of the black vote in this election,"
David Maraniss, Washington Post 19 Oct. 1991 page A03.]
If they had to choose between Duke and anyone, it
wouldn't be the neo-Nazi and Ku Klux Klan wizard Duke.
(And, ignoring race, most Edwards Democrats
presumably would have found the moderate and former Democrat Roemer preferable to the
archconservative Duke.)

If these polls were correct, this election exhibited these 7 "paradoxes":

With Louisiana's runoff system, the beats-all winner
Roemer lost (eliminated in the first round)!

Also, Roemer would have lost in a straight plurality
election (with no runoff), i.e. just the first-round voting.

The Duke voters would have been better off
"betraying their favorite"
Duke by instead voting Roemer. That would have caused their second choice
Roemer to win, an improvement
(in their view) versus what actually happened. Dishonesty (would have) paid!

Also, if these Duke voters favoring Roemer>Edwards had simply not voted,
then Roemer would have won. That's a "No Show paradox" – they'd
have been better off not voting.

Thus Duke was an "IRV spoiler":
by voting Duke, his supporters
actually caused both him and their second choice Roemer both to lose.
This is just like how Nader voters caused both Nader
and their second choice Gore both to lose
in the USA's Florida 2000 presidential election – Nader was the "spoiler" there,
albeit that election was conducted using plurality rather than the IRV system.

Duke would have lost a head-to-head race versus every major rival
(perhaps even every rival),
but he made it into the runoff while all those rivals did not.

And if this lose-to-all loser had dropped out,
then Roemer would have won, but by
running, Duke made Edwards (whom Duke voters disliked!) win.

What about an 8th kind of paradox:
non-monotonicity?
To see another
non-monotonic IRV election, check
Ireland 1990.
Actually that election exhibits participation-failure and favorite-betrayal pathologies
but is monotonic.
It only exhibits non-monotonicity if you alter the scenario by adding some
extra Currie voters. That scenario is a "hybrid" of non-monotonicity and no-show paradoxes:
Lenihan's supporters made Lenihan
lose by voting for him – if they had instead voted for Lenihan's
most-hated rival Currie, then
Lenihan would have won!
A (pure) non-monotonic IRV election is Burlington VT 2009.
You also can see a simple artificial incredibly-crazy IRV
election example.

W.Poundstone offers this argument that the Louisiana 1991
election also suffered from monotonicity
failure:

Suppose that a group of Duke supporters switch their allegiance to
Edwards. (I'm not claiming this was politically or psychologically
very credible
–
only that it's a possibility that would have triggered
nonmonotonic behavior.) Moving 5.3% of the total electorate from
Duke to Edwards, produces this outcome for the first-round vote
(these do not total 100% because we are not listing the other candidates):

(Hypothetical)

Edwards

39.1%

Roemer

26.5%

Duke

26.4%

Then Duke rather than Roemer is eliminated, and – if the remaining
26.4% of the voters (all of whom favor Duke) then happened to
prefer Roemer over Edwards enough –
then Roemer would win.
I.e: that 5.3% changing their vote to Edwards would have prevented Edwards' victory!

This indeed demonstrates monotonicity failure.

Approval & Range voting

Approval and especially
Range
clearly would have outperformed runoff (and instant runoff) in this election;
Duke would have had no chance at victory,
and
the winner would have been Roemer.

Approval ratings in 1991 polls

Name

Approval

Disapproval

Roemer

58%

36%

Edwards

34%

59%

Duke

10%

67%

In a 30 October 1991 US nationwide Gallup telephone poll,
10% said they had a "favorable" opinion of Duke,
versus 67% "unfavorable."
Admittedly Lousianans seemed to like him more than the USA as a whole,
but even so I think Duke would have ≤33% approval, and certainly ≤39%
which was his official-runoff total and probably includes many who did not approve him
(since certainly Edwards' official-runoff total does).
In a 1991 University of New Orleans telephone poll of random Louisianans,
20% "strongly approved" and 38% "approved" of Roemer (total 58%), versus
21% "disapproving" and 15% "strongly disapproving" (total 36%).
Also in twelve 1987 polls Roemer had gotten 39-60% approval versus 30-58% disapproval
and even the lowest among those twelve (39%) still would have been enough to make him win.
Note Roemer was the only candidate more approved than disapproved.
In 1991,
a Mason Dixon Political Media research poll of 816 likely voters found
35% approved and 60% disapproved Edwards;
and SRC/Univ. of New Orleans poll of 725 registered voters found
40% approved and 49% disapproved;
an SE LA Univ. poll of 700 registered voters found
28% approved and 59% disapproved;
and finally a Renwick/Baton Rouge Advocate Poll of 988 registered voters
found 32% "favorable" versus 65% "unfavorable."
Averaging over all four of those polls (i.e. viewing them as a single poll of 3229 people)
we get a net
approval=34%
disapproval=59%
rating for Edwards.
Also in a 2002 look back
at Edwin Edwards, the University of New Orleans Survey Research Center
asked Louisianans whether they
"approve or disapprove of the job that
Edwin Edwards did as governor?".
40.1% approved and 45.7% disapproved, and I believe Edwards generally had a worse approval rating
in ≈1990 than in 2002.
So although these polls unfortunately
were of different people at different times with different wordings and hence are not optimally
comparable, to the (large) extent they are valid,
they indicate Roemer easily would have won an approval-voting
election.

Duke enjoyed
a vote-split among the non-Duke candidates. With range and approval voting, "vote splitting"
does not exist. And range and approval are monotonic, never exhibit "favorite betrayal,"
and always (under
certain fairly plausible assumptions about strategic voter behavior)
elect beats-all winners like Roemer.

A range-voting-style telephone poll of 745 Louisianans actually was
done by the University of New Orleans
in 1991. I warn you that I am not exactly sure what is
being reported by them in the concise summary below.
(I requested details but they never responded.)
But to the extent it is valid, it concluded Roemer would have won with range voting.

On a scale from 0 to 100, where 0 is very cool feelings and 100
represents very warm feelings, what would you rate your feelings about
Buddy Roemer, Edwin Edwards, or David Duke in the election for
governor?
RESULTS:
Roemer 30%
Edwards 28
Duke 24
Contact Information: Survey Research Center
University of New Orleans
New Orleans, LA 70148
(504) 286-6459 or 246-3999

Main Sources (besides polls)

John Maginnis: Cross to Bear,
Darkhorse Press 1992.
(This is an entire book just about this one election; it has a
web page.)